The particle filtering technique is known, see Arulampalam, IEEE Transactions on Signal Processing Vol. 50, No. 2, February 2002, pp 174188 “A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking”
A particle filter algorithm may be summarised as including the following key steps:    1. A set of particles are maintained that are candidate representatives of a system state. A weight is assigned to each particle, and an estimate of the state is obtained by the weighted sum of the particles (a non-analytic probability distribution function (pdf)).    2. A recursive operation is carried out that has two phases: prediction and update.    3. For prediction, at time t=k, the pdf is known at the previous time instant t=k−1. A system model is used to predict the state at time t=k    4. For update, at time t=k, a measurement of the system becomes available, which is used to update the pdf that was calculated in the prediction phase. During update, the particles may be resampled to remove particles with small weight.    5. return to 3.
An objective of particle filtering may be to track a variable of interest as it evolves over time, for example the state of an aircraft, by means of a series of observations with a number of sensors. The observations typically have a non-Gaussian measurement function. The technique is a sequential Monte Carlo method, in which a set of state trajectories (or particles) are maintained that are candidate representatives of a system state. When a new observation is made, each trajectory is extended and weights are assigned to each particle according to the likelihood of the state it represents given the measurement. A new particle population is generated to replace the old one by resampling from the old particle population in proportion to the weights.
Algorithms for solving problems over a network fall into three classes:
Centralised algorithms: Centralised algorithms require that all data be sent to a single node. The processing occurs at that node and the assignment solution is sent out to all nodes. Centralised algorithms are not robust and do not scale well with network size. They are not robust since the removal of the central node causes complete failure. They do not scale well as the number of messages that must be sent down a given link will tend to grow with network size (or the number of links to the central node will grow).
Distributed algorithms: Distributed algorithms require that all data be sent to all nodes. Each node is then able to process the data to arrive at the optimal solution. Distributed algorithms are robust, but not scaleable.
Decentralised algorithms: This applies to networks wherein each node is connected for receiving or transmitting information to selected other nodes of the network, usually neighbouring nodes. Decentralised algorithms include data fusion (for the purposes of this specification, data fusion is intended to mean processing of information) at each node before information is passed on to connected nodes. This allows some of the processing necessary to reach an optimal answer at a particular node, to be carried out at neighbouring nodes, and avoids the requirement that all data be sent to all nodes. Decentralised algorithms are robust and scaleable. A decentralised network has the following properties:                1. There is no single central decision centre; no one node should be central to the successful operation of the network.        2. Nodes do not have any global knowledge of network topology, or size;        nodes should only know about connections in their own neighborhood.        
There are published methods for decentralising the particle filter, where data processing is carried out locally at selected nodes of a network of nodes, each node corresponding for example to a sensor. The results of the data processing are exchanged between neighbouring nodes. The decentralised methods published in the literature, achieve decentralization through a compact representation of the particle filter's particle population; see:
M. Rosencrantz, G. Gordon, S. Thrun, “Decentralized Sensor Fusion With Distributed Particle Filters”, Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03), Morgan Kaufmann Publishers, San Francisco, Calif., 2003, pp 493-500 M. Coates, “Distributed Particle Filters For Sensor Networks”, Information Processing In Sensor Networks Proceedings of the third international symposium on Information processing in sensor networks, Berkeley, Calif., USA, 2004, pp 99-107
The problem with these published methods is that they do not provide a robust representation, that there is no quantitative measure of the quality of the representation achieved, and that the representations do not lend themselves well to inclusion in a decentralized tracking scheme.
The use of a mixture of Gaussian distributions as a compact representation for a non-Gaussian probability distribution in decentralised tracking is described in S. Kumar and B. Upcroft, “ANSWER II Interim Progress Report: Algorithmic Design” Department of Aerospace, Mechatronic and Mechanical Engineering, University of Sydney, July 2004. This work makes no mention of application to particle filtering, and involves the assimilation of multiple Gaussian mixture distributions that is identified as a drawback with large computational requirements.